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Measurement-Cost Triage for Non-Markovian Entanglement Diagnostics in Hyperentangled Photonic Qubits

Authors: Jakob, Matthias;

Measurement-Cost Triage for Non-Markovian Entanglement Diagnostics in Hyperentangled Photonic Qubits

Abstract

We formulate a layer-resolved diagnostic protocol for separating different kinds of quantuminformationcontent in a hyperentangled four-qubit state undergoing local non-Markovianpure dephasing. The protocol uses Bell-sector coherence flow as a low-cost entrance test forcandidate backflow windows, but does not identify this signal with entanglement recovery.Informative windows are then promoted to local complementarity, pair-concurrence, andsimultaneous all-cut negative-partial-transpose (NPT) diagnostics. For the benchmark familystudied here, the pair concurrence CAB(t), the local complementarity defect DA(t), and thewhite-noise visibility threshold vc(t) of the all-cut NPT layer have closed-form expressions.These relations show explicitly that coherence backflow, bipartite entanglement recovery,local budget redistribution, and all-cut NPT activation are distinct diagnostic statements.Robustness checks under controlled-phase, visibility, reservoir-parameter, and small stateperturbationvariations support the use of the hierarchy as a quantum-information decisionprotocol rather than as a single state measure. The result is not a new entanglement ornon-Markovianity monotone; it is an operational way to decide which information layer iscertified by a given measurement record and when richer reconstructions are justified.

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